George D. Swanson

Computerized estimation of lactate threshold

Traditional approaches to estimating a lactate threshold during a progressive exercise test have utilized visual inspection of the data. We describe a computerized approach which utilizes a log-log transformation to yield two approximately linear segments. Linear regression lines are fit to these segments and the intersection of the two lines yields an estimate of the lactate threshold. An approximate 95% confidence interval is also generated.

Sensitivity of Breath-to-Breath Gas Exchange Measurements to Expiratory Flow Errors

During expiration, fluctuations in gas composition, water vapor, and temperature result in flowmeter errors when the flowmeter is calibrated for a given ambient inspiratory gas. In this paper, we indicate that alternative analytical methods of caleulating breath-to-breath gas exchange exhibit differing sensitivities to this error. A theoretical sensitivity analysis is verified by O2 consumption records from rest to exhausting exercise. We conclude that an error sensitivity of less than one is achieved by a method that incorporates measurements of nitrogen flow into and out of the lung, and includes the analysis of breath-to-breath changes in lung volume.

Biological signal conditioning for system identification

The use of mathematical models to characterize physiological systems attempts to summarize how a system behaves in terms of its internal structure. Thus the models should be isomorphic to the underlying physiological structure, and the model parameters must be estimated from input-output observations of the system. The model must be identifiable, in the sense that a unique parameter set exists and that parameter set is resolvable in the presence of noise. This paper considers these identifiability issues with specific emphasis on the effect of biological observation noise in degrading the parameter estimation process. It is shown that conditioning the output signal via design of the experimental input can minimize this degradation. These concepts are applied to metabolic and respiratory system studies.

Uptake of nitrous oxide by man

Because of discrepancy in reports concerning the rate of uptake of nitrous oxide by man, it seemed desirable to measure this factor when automatic control of concentrations and rapid computer measurement of breath to breath uptake became available. Six subjects inhaled 25 per cent nitrous oxide for two hours. Total uptake and alveolar uptake were determined. The total inhaled uptake, adjusted for a 70 kg subject inhaling 75 per cent nitrous oxide, corresponded well with an absorption of about 1000 ml the first minute. After a wash-in period of less than four minutes, the alveolar uptake, which at that time and subsequently equaled the total uptake, decreased approximately according to the square root of time in minutes. Considerable variation appeared between individuals, but each course approximated the same type of decrease. Absorption continued to occur during the two hour period of observation.RésuméC’est en constatant la discordance entre les résultats des études de mesure de la captation du protoxyde d’azote chez l’homme qu’il est apparu désirable de reprender ces mesures de façon plus précise en utilisant le contrôle automatique des concentration avec la mesure rapide de la captation par cycle respiratoire. On a fait inhaler du protoxyde d’azote à 25 pour cent à six sujets. Les captations totale et alvéolaire ont été mesurées. La captation inhalée totale ajustée pour un sujet de 70 kg inspirant une concentration de protoxyde d’azote à 75 pour cent correspondait bien avec une absorption de 1000 ml à la première minute. Après une période de moins de quatre minutes, la captation alvéolaire qui à ce moment et subséquemment égalait la captation totale, a diminué à une vitesse se rapprochant la racine carrée du temps en minute. Les variations individuelles ont été considérables mais la forme de la courbe de déclin était à peu prés identique chez tous les sujets. L’absorption s’est continuée pendant la période de deux heures.

Statistical identification of compartmental models with application to plasma protein kinetics

A numerical method for fitting linear compartmental models to data is presented which is similar to the method proposed by Jennrich and Bright (R. I. Jennrich and P. B. Bright, Technometrics 18, 385 (1976] and Feldman (H. A. Feldman. Amer. J. Physiol. 233, R1 (1977] but avoids some of the numerical difficulties. The method is direct and does not use numerical integration thereby avoiding time consuming and expensive calculations. Emphasis is on statistical procedures for model selection. In addition to the usual F tests for comparing two models, Akaikes Information Criterion (AIC) is introduced for choosing from among several models. The combined use AIC with an F test, chi-square test, or confidence intervals on estimated parameters gives a practical method to obtain a balance between underfitting and overfitting. Application to models of plasma protein kinetics illustrates the method.

Smoothing polynomial splines for bivariate data

An extension of the smoothing polynomial spline to fit bivariate response data is presented. The data are modeled as integrated random walks with observational errors. Correlation can exist in the random walks, the observational errors, or both. The Kalman filter is used to calculate the log likelihood of the data as a function of the unknown parameters in the covariance matrices, and nonlinear optimization is used to obtain maximum likelihood estimates of the parameters. A modification of the Kalman filter is used at the beginning of the data to allow the use of diffuse (noninformative) priors. This model is applied to the problem of characterizing gas exchange time series of exercising subjects.

Optimal frequency locations for estimating model parameters in studies on respiratory control.

Sinusoidal work rate inputs yield a dynamic ventilatory response which can be fitted to a mathematical model. The model structure leads to inferences about the underlying physiology of the respiratory control mechanism. A particular problem of interest in model parameter estimation concerns the location of the test frequencies. The effects of estimating the parameters of a relatively complex model developed by Fujihara et al. using arbitrary frequency locations from a study by Casaburi et al. versus using the frequencies derived from an optimization method presented in a recent paper by Engeman et al. were examined. The Fujihara model is indicated to be much more likely to be justified when optimal sinusoids are used to generate the data than when Casaburis arbitrary frequencies are used. The implications are that more descriptive models of respiratory control may be developed with the aid of optimal frequency design for the input sinusoids.

A computerized mass spectrometer and flowmeter system for respiratory gas measurements

Instrumentation systems for breath-to-breath analysis of respiratory gas exchange have been faulted by phase lags between various flow and composition signals and by difficulties in gathering and processing large amounts of data. The system described here represents an attempt to overcome these problems. Phase delays have been minimized by using a direct, piezoelectrically operated mass spectrometer inlet rather than an inlet capillary, by locating the mass spectrometer inlet and flow sensors in the same plane, and by incorporating design features which enhance the mass spectrometer response. Convenience in system operation and data analysis has been enhanced by integrating a computer into the system design so that the computer performs on-line data analysis and control functions and provides the primary interface between the experimenter and the instruments. Miniaturization of the instruments permits close coupling to an exercising subject.

Pulmonary Training May Alter Exertional Dyspnea and Fatigue Via an Exercise-Like Training Effect of a Lowered Heart Rate

Recent small studies utilizing respiratory muscle training have incorporated a voluntary hyperventilation maneuver via an open chamber gas mixing system (to maintain isocapnic conditions). These studies suggest that the time to exercise exhaustion may be increased at exercise levels near but above the so-called anaerobic threshold after several weeks of intense pulmonary training (1,2).

Redundancy Structures in Respiratory Control

The observation that arterial CO2 tension is regulated (remains at the resting value) under a metabolic CO2 load via exercise, but increases under an airway CO2 load via inspiratory CO2, has motivated numerous theories about the structure of the respiratory controller. This respiratory control system behavior appears to be most consistent with a feedforward/feedback control system structure.1 The peripheral chemoreceptors (carotid body) and indirectly central brain chemoreceptors act as feedback mechanisms with respect to the regulation of arterial CO2 tension. Feedforward mechanisms (signals related to metabolic CO2 production during exercise) are more controversial. Part of this controversy relates to the traditional “search” for a “single” mechanism that will explain the exercise hyperpnea response.2 However, in general, biological systems are characterized by redundancy, suggesting that many “signals” may be combined to form an appropriate feedforward stimulus.